Atmosphere turbulent diffusion

Long, P. E., and Pepper, D. W., A comparison of six numerical schemes for calculating the advection of atmospheric pollution, in "Proceedings of the Third Symposium on Atmospheric Turbulence, Diffusion and Air Quality." American Meteorological Societv, Boston, 1976, pp. 181-186. 

Huber, A. H., and Snyder, W. H., Building wake effects on short stack effluents, pp. 235-242 in Preprints, Third Symposium on Atmospheric Turbulence, Diffusion and Air Quality. October 19-22, 1976, Raleigh, NC. American Meteorological Society, Boston, 1976. 

The energy of large and medium-size eddies can be characterized by the turbulent diffusion coefficient. A, m-/s. This parameter is similar to the parameter used by Richardson to describe turbulent diffusion of clouds in the atmosphere. Turbulent diffusion affects heat and mass transfer between different zones in the room, and thus affects temperature and contaminant distribution in the room (e.g., temperature and contaminant stratification along the room height—see Chapter 8). Also, the turbulent diffusion coefficient is used in local exhaust design (Section 7.6). 

In natural systems (lakes, oceans, atmosphere) turbulent diffusion is usually anisotropic (i.e., much larger in the horizontal than vertical direction). There are two main reasons for that observation (1) the extension of natural systems in the horizontal is usually much larger than in the vertical. Thus, the turbulent structures (often called eddies) that correspond to the mean free paths of random motions often look like pancakes that is, they are flat along the vertical axis and mainly extended along the horizontal axes. (2) Often the atmosphere or the water body in a lake or ocean is density stratified (i.e., the density increases with depth). This compresses the eddies even further in the vertical. Gravitational forces keep the water parcels from moving too far away from the depth where they are neutrally buoyant, that is, where they have the same density as their environment. Thus, the anisotropic shape of the eddies results in turbulent diffusivities which differ in size along different spatial directions. 

The two idealized source types commonly used in atmospheric turbulent diffusion are the instantaneous point source and the continuous point source. An instantaneous point source... 

This solution describes a plume with a Gaussian distribution of poUutant concentrations, such as that in Figure 5, where (y (x) and (y (x) are the standard deviations of the mean concentration in thejy and directions. The standard deviations are the directional diffusion parameters, and are assumed to be related simply to the turbulent diffusivities, and K. In practice, Ct (A) and (y (x) are functions of x, U, and atmospheric stability (2,31—33). 

Early models used a value for that remained constant throughout the day. However, measurements show that the deposition velocity increases during the day as surface heating increases atmospheric turbulence and hence diffusion, and plant stomatal activity increases (50—52). More recent models take this variation of into account. In one approach, the first step is to estimate the upper limit for in terms of the transport processes alone. This value is then modified to account for surface interaction, because the earth s surface is not a perfect sink for all pollutants. This method has led to what is referred to as the resistance model (52,53) that represents as the analogue of an electrical conductance... 

Wind speed has velocity components in all directions so that there are vertical motions as well as horizontal ones. These random motions of widely different scales and periods are essentially responsible for the movement and diffusion of pollutants about the mean downwind path. These motions can be considered atmospheric turbulence. If the scale of a turbulent motion (i.e., the size of an eddy) is larger than the size of the pollutant plume in its vicinity, the eddy will move that portion of the plume. If an eddy is smaller than the plume, its effect will be to difhise or spread out the plume. This diffusion caused by eddy motion is widely variable in the atmosphere, blit even when the effect of this diffusion is least, it is in the vicinity of three orders of magnitude greater than diffusion by molecular action alone. 

Briggs, G. A., "Diffusion Estimation for Small Emissions." Atmospheric Turbulence and Diffusion Laboratory, Contribution File No. 79. (draft). Oak Ridge, TN, 1973. 

The Gaussian Plume Model is the most well-known and simplest scheme to estimate atmospheric dispersion. This is a mathematical model which has been formulated on the assumption that horizontal advection is balanced by vertical and transverse turbulent diffusion and terms arising from creation of depletion of species i by various internal sources or sinks. In the wind-oriented coordinate system, the conservation of species mass equation takes the following form ... 

Fig. 4-15 Orders of magnitude of the average vertical molecular or turbulent diffusivity (whichever is largest) through the atmosphere, oceans, and uppermost layer of ocean sediments.

G. A. Briggs, Diffusion Estimation for Small Emissions, Report ATDL-106 (Washington, DC Air Resources, Atmospheric Turbulence, and Diffusion Laboratory, Environmental Research Laboratories, 1974). 

General References Britter and McQuaid, Workbook on the Dispersion of Dense Gases, Health and Safety Executive Report 17/1988, Sheffield, U.K., 1988. Mannan, Lees Loss Prevention in the Process Industries, 3d ed., Chap. 15, Elsevier Butterworth-Heinemann, Oxford, U.K., 2005. Panofsky and Dutton, Atmospheric Turbulence, Wiley, New York, 1984. Pasquill and Smith, Atmospheric Diffusion, 3d ed., Ellis Horwood Limited, Chichester, U.K., 1983. Seinfeld, Atmospheric Chemistry and Physics of Air Pollution, Chaps. 12-15, Wiley, New York, 1986. Turner, Workbook of Atmospheric Dispersion Estimates, U.S. Department of Health, Education, and Welfare, 1970. 

The Eulerian approach to turbulent diffusion was shown to lead to the atmospheric diffusion equation (2.19) ... 

The Gaussian expressions are not expected to be valid descriptions of turbulent diffusion close to the surface because of spatial inhomogeneities in the mean wind and the turbulence. To deal with diffusion in layers near the surface, recourse is generally had to the atmospheric diffusion equation, in which, as we have noted, the key problem is proper specification of the spatial dependence of the mean velocity and eddy difiusivities. Under steady-state conditions, turbulent diffusion in the direction of the mean wind is usually neglected (the slender-plume approximation), and if the wind direction coincides with the x axis, then = 0. Thus, it is necessary to specify only the lateral (Kyy) and vertical coefficients. It is generally assumed that horizontal homogeneity exists so that u, Kyy, and Ka are independent of y. Hence, Eq. (2.19) becomes... 

Briggs, G. A. (1974). Diffusion estimation for small emissions. In Envirorunental Research Laboratories, Air Resources Atmosphere Turbulence and Diffusion Laboratory 1973 Annual Report, USAEC Rep. ATDL-106. Natl. Oceanic Atmos. Adm., Washington, D.C. 

Volatilization (also referred to as vaporization or evaporation) is the conversion of a chemical from the sohd or hquid phase to a gas or vapor phase. The partitioning of a volatile compound in the subsurface environment comprises two distinct patterns volatilization of contaminant molecules (from the liquid, sohd, or adsorbed phase) and dispersion of the resulting vapors in the subsurface gas phase or the overlying atmosphere by diffusive and turbulent mixing. Even though the two processes are fundamentally different and controlled by different chemical and environmental factors, they are not wholly independent under natural conditions only by integrating their effects can volatilization be characterized. 

Schumann, U. 1989. Large eddy simulation of turbulent diffusion with chemical reactions in the convective boundary layer. Atmospheric Environment 23(8) 1713-26. 

Chapters Turbulent Diffusion. Turbulent diffusion is an important transport mechanism in the atmosphere, oceans, lakes, estuaries, and rivers. In fact, most of the atmosphere and surface waters of the Earth are turbulent. If you are going to work in any of these systems, it will be important to have at least a working knowledge of turbulent diffusion. 

Diffusion Flame. When a slow stream of fuel g s flows from a tube into the atmosphere, air diffuses across the boundary of the stream and Brms an envelope of expl mixture around a core of gas. The core decreases in height until it disappears at some distance above the tube. It thus assumes the shape of a cone. On ignition, a flame front spreads thru the mixture and stabilizes itself around the cooe of fuel gas. The hydrocarbons in common fuel gases crack to form free C H. The shell of carbon-bearing gas so formed gives such flames their luminosity Turbulent Jet Flame. When a gas stream issues from an orifice above a certain critical velocity, it breaks up into a turbulent jet that entrains the surrounding air. The flame of such a jet consists of random patches of combustion and no cohesive combustion surface exists... 

The relation between length and time scales of diffusion, calculated from the Einstein-Smoluchowski law (Eq. 18-8), are shown in Fig. 18.11 for diffusivities between 10 10 cm2s 1 (helium in solid KC1) and 108 cm2s (horizontal turbulent diffusion in the atmosphere). Note that the relevant time scales extend from less than a millisecond to more than a million years while the spatial scales vary between 1 micrometer and a hundred kilometers. The fact that all these situations can be described by the same gradient-flux law (Eq. 18-6) demonstrates the great power of this concept. 

Hints and Help Assume that as a first approximation horizontal turbulent diffusivity can be considered to be isotropic, that is, Ex = Ey= 2 x 104cm2s 1. Disregard the loss of HCB across the thermocline and to the atmosphere. In Chapter 22.3 we will see that because of horizontal water currents horizontal diffusion is, in fact, not isotropic. Nonetheless the above approximation yields reasonable results. Finally, note that in order to keep the total mass of HCB constant, CQ (t) must decrease as R(t) grows such that CaR2= constant. 

While molecular diffusivity is commonly independent of direction (isotropic, to use the correct expression), turbulent diffusivity in the horizontal direction is usually much larger than vertical diffusion. One reason is the involved spatial scales. In the troposphere (the lower part of the atmosphere) and in surface waters, the vertical distances that are available for the development of turbulent structures, that is, of eddies, are generally smaller than the horizontal distances. Thus, for pure geometrical reasons the eddies are like flat pancakes. Needless to say, they are more effective in turbulent mixing along their larger axes than along their smaller vertical extension. 

Radioactive or stable isotopes of noble gases are also used to determine vertical turbulent diffusion in natural water bodies. For instance, the decay of tritium (3H)— either produced by cosmic rays in the atmosphere or introduced into the hydrosphere by anthropogenic sources—causes the natural stable isotope ratio of helium, 3He/ 4He, to increase. Only if water contacts the atmosphere can the helium ratio be set back to its atmospheric equilibrium value. Thus the combined measurement of the 3H-concentration and the 3He/4He ratio yields information on the so-called water age, that is, the time since the analyzed water was last exposed to the atmosphere (Aeschbach-Hertig et al., 1996). The vertical distribution of water age in lakes and oceans allows us to quantify vertical mixing. 

Explain the difference between the dispersion coefficient, dis, in a river and in the atmosphere. How is dis related to the mean advection velocity and to lateral turbulent diffusivity in each case ... 

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